How many different five letter words starting with a vowel can be formed from the letters of the word $\mathrm{EQUATION}?$

In how many ways can $8$ boys and $7$ girls be photographed if girls are to sit on chairs in a row and the boys stand in a row behind them?

[Enter the value as one single integer]

In how many ways can $8$ boys and $7$ girls be photographed if girls sit on even numbered chairs and boys sit on odd numbered chairs and there are $15$ chairs in a row?

[Enter the value as one single integer]

In how many ways can $8$ boys and $7$ girls be photographed if there are $15$ chairs in a row and there is no restriction?

[Enter the value in factorial format]